Tuesday Apr. 12, 2011
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HW Assignment #5 pt. 2 has been graded and was returned in class today together with a set of answers.

No new assignments yet.

Some followup on a few items from last Thursday's class.

I mentioned that lightning has on at least one occasion lightning has either delayed or interrupted a football game at Arizona Stadium.  I found the following article while putting last Thursday's notes online.  "Lightning Safety and Large Stadiums," J. Gratz and E. Noble, Bull. Am. Meteorol. Soc., 87, 1187-1194, 2006. (link to a PDF file)

You should be aware of the National Lightning Safety Institute , an organization that is dedicated to providing accurate lightning safety information and interested in lightning safety education.

I don't think I mentioned The 30/30 Rule.  Basically if there is less than 30 seconds between a lightning flash and the sound of the thunder, that lightning discharge is close enough to present a risk to you.  You should be under cover.  You should wait 30 minutes after the last lightning discharge from a thunderstorm before concluding that the storm no longer presents a lightning hazard to you.

For the next 2 or 3 classes we will be looking at some of the techniques used to locate lightning.  Today we'll concentrate on magnetic direction finding and the National Lightning Detection Network.

Before getting into the details here's a diagram of a portion of the radio frequency spectrum

Today we'll be looking at techniques used in the National Lightning Detection Network (NLDN) to locate lightning strikes to ground.  Wideband sensors that operate from 10s kHz to a few 100s of kilohertz (to just below the start of the AM radio band at 550 kHz) are used.  We'll be concerned mainly with signals from return strokes.  MDF stands for magnetic direction finding.  TOA is time of arrival.

We may also discuss a new system for locating lightning on a global scale.  This senses mainly VLF signals that have propagated over large distances (1000s of km).

TOA and interferometry that detect VHF frequency emissions are able to locate and follow channel development in the cloud.  We'll look at this on Thursday.

A magnetic direction finder system uses two orthogonal loop antennas.  One loop is shown below.  A distant lightning strike produces a horizontal field that passes through the antenna.
 
Faraday's law states that the voltage across the open ends of the loop antenna will be equal to the time rate of change of the flux through the antenna.  We'll assume that B is uniform across the area of the antenna so that it can be taken out of the integral above.  This signal can be integrated to a signal that is proportional to B.  The important point to take from this figure is that the output signal from the antenna will depend on the location of the strike with respect to the plane of the antenna.  This is developed further in the figure below.

In the picture above we've assumed an upward pointing return stroke such as would come from a negative cloud-to-ground discharge.  For a positive cloud-to-ground strike, the current would point downward, and the signal from the loop antenna would have the opposite polarity.  You need to record electric fields together with magnetic fields to be able to determine the polarity of the return stroke.



The lightning is located north of the antenna in (a), east in (b) and south in (c).  You'd measure a large positive signal coming from the loop in (a), zero signal in (b) because the B field doesn't pass through the antenna (B is perpendicular to the normal to the loop), and a strong negative signal in (c).  We've assumed a negative cloud-to-ground discharge (upward pointing current) in each of these examples.

Next we'll look at how the bearing angle to a lightning strike can be determined using the signals from two orthogonal loops.


We want to be able to determine theta using measurements from a NS loop and EW loop antennas.  We'll look at the output from the NS loop first.

The output signal is proportional to the cosine of the bearing angle. 

The signal from the EW loop is proportional to the sine of the bearing angle.


The bearing angle can be determined by taking the inverse tangent of the ratio of the two loop antenna signals.


Examples of NS signals and EW signals that you would expect to see for strikes to the NE, SSE, and WNW of the orthogonal loop antenna.  And something that I didn't mention in class: the square root of the sum of the squares of the two signals gives you the B field amplitude.

Once the distance to the discharge is determined, the B field ampltitude (assumed to be purely radiation field) can be used in the transmission line model to estimate the peak current in the stroke.  Of course you could also use the E field to estimate peak current.

A class handout showing the orthogonal loop antenna used in the original lightning direction finding system was distributed in class.  The figures can be found in "Lightning Direction-Finding Systems for Forest Fire Detection," E.P. Krider, R.C. Noggle, A.E. Pifer, and D.L. Vance, Bull. Am. Meteorol. Soc., 61, 980-986, 1980. (link to a PDF file).  The original antenna was a PVC pipe structure perhaps 8 feet tall.  A picture of the next generation antenna, maybe only 2 or 3 feet tall is also shown in the publication.  It is worth mentioning that the original DF systems were being used for forest fire prevention in Alaska.

The publication cited above also contains examples of typical lightning return stroke radiation field waveforms (the E and B radiation field waveforms are essentially identical).  An example of a large amplitude signal from a cloud discharge was also shown.  Typical cloud-to-ground and cloud discharge waveshapes are sketched below

Once a lightning signal is detected by a magnetic direction finder sensor, the waveform must pass a series of waveshape tests.  The main objective being to discriminate between return stroke waveforms and waveforms from large amplitude cloud discharges.  We have implicity been assuming in our discussion that the lightning channel is vertically oriented.  This is a pretty reasonable assumption for cloud-to-ground discharges, especially when the return stroke is close to the ground.  Channel tilt will add signficant errors to the estimate of bearing angle.  Cloud discharge channels can be tilted and are often essentially horizontal. 

If the waveform passes the waveshape tests, the peak ampltitudes of the NS and the EW signals are determined.  At the time of peak signal, the return stroke is probably within about 100 m of the ground.  Estimating the bearing angle at this time is advantageous because you eliminate the effects of channel branches, the channel is often fairly straight and vertical near the ground, and you're determining a direction to where the return stroke struck the ground.

Once bearing angle estimates are made at multiple DF sensor locations, you can then triangulate to locate the lightning strike point.  Errors in the bearing angle estimate of course lead to uncertainty in the lightning strike location.

Here we see the location determined using bearing angles from only 2 sensors (the minimum number required).  In the current NLDN network return strokes with a current of 25 kA would be detected by 6-8 sensors.  There are sophisticated methods for determining the optimal location with redundant data like that.

Large location errors can be present when a lightning strike is on or near a baseline between two sensors.





Of course with redundant data like you have in the NLDN other sensors would be of the baseline and would provide more accurate location information.

It became evident in early incarnations of the NLDN that sufficient location accuracy would not be possible using magnetic direction finding alone unless sensors were on the order of 100 km apart.  Operation of a network with that kind of density would be too expensive.  In the current network sensors are 300 to 350 km apart (there are just over 100 sensors I believe in the current network).